A manufacturer produced x percent more video cameras in 1994 than in

Question

A manufacturer produced x percent more video cameras in 1994 than in 1993 and y percent more in 1995 than in 1994. If the manufacturer produced 1,000 video cameras in 1993, how many video cameras did the manufacturer produce in 1995?

(1) xy = 20
(2) x + y + xy/100 = 9.2

(1) xy = 20
(2) x + y + xy/100 = 9.2

GyanOne · Accepted Answer

The question has one critical word missing. Am assuming as follows: 
A manufacturer produced x percent  more  video cameras in 1994 than in 1993 and y percent more in 1995 than in 1994. If he produced 1000 video cameras in 1993, how many did he produce in 1995?

Video cameras produced in 1995 = 1000 * (1+x/100) * (1+y/100) 
= 1000 * (1 + x/100 + y/100 + xy/10000) cameras 
= 1000 + 1000/100 (x + y + xy/100) cameras
= 1000 + 10 (x + y + xy/100) cameras

Using statement (1), we know xy but not know x and y separately. Insufficient. 
Using statement (2), we know x + y + xy/100 and so can calculate the expression above. Sufficient.

(B) it is.

walker · Answer

B

N=1000*\frac{(100+x)}{100}*\frac{(100+y)}{100}=10*(100+x+y+\frac{xy}{100})

paddyboy · Answer

B.

Take,
m = 2003 production
n = 2004 production
p = 2005 production

n = (100 + x)*m/100 -- 1
p = (100 + y)*n/100 -- 2

Substituting 1 in 2,
=> p = (100 + x)(100 + y)*m/(100*100)
=> p = (1 + x/100 + y/100 + xy/10000)*m
=> p = (100 + x + y + xy/100)*m/100

#1. xy = 20

Insufficient; as we get
p = (100 + x + y + 20/100)*m/100 => still have 2 unknowns

#2. x + y + xy/100 = 9.2

Sufficient; as we get
p = (100 + 9.2)*m/100 => no more unknowns

mrmikec · Answer

I got the following:

1993 = m
1994 = n
1995 = p

1994 = ((100+x)/100)m
1995 = ((100+y)/100)n

sub N

1995 = ((100+x)/100)((100+y)/100)m

= ((10000+100x+100y+xy)/10000)m

 = ((1+x/100+y/100+xy/10000))m 

C1. xy = 20
INSUFFICENT

C2. x+y+xy/100= 9.2
rewritten as

x/100+y/100+xy/10000 = 9.2(1/100)=9.2/100

Thus
subing condition2 into the underlined statement gets me

( 1+ 0.092)m = ??

What happens to m? We just assume its 100.

superman · Answer

This is tricky but simple

Lets the number of increase in camera be m for 1993 to 1994

==> m = 1000 * x/100 = 10x

Lets the number of increase in camera be n for 1994 to 1995

==> n = (1000 + 10x) * y/100 = (100 + x) * y/10 = 10y + xy/10

Now the cameras in 1995 = 1000 + a + b = 1000 + 10x + 10y + xy/10 = 10(100+x+y+xy/100)

Now using stmt 2 we can solve the above equation hence Stmt 2 is sufficient and hence answer is B

Note from stmt 1 we wont know values of x and y

fozzzy · Answer

1993 
1000

1994 
 1000( 1+\frac{x}{100})

1995
 1000(1+\frac{x}{100)}(1+\frac{y}{100})

solve for 1995 and take  \frac{1}{100}  common you will get statement 2 sufficient!

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/the-annual-re ... 89184.html https://gmatclub.com/forum/between-1980- ... 45738.html

PiyushK · Answer

I got E because of typo made in the question.

Original question :: A manufacturer produced x percent   more   video cameras in 1994 than in 1993
Typo :: A manufacturer produced x percent ____ video cameras in 1994 than in 1993

Bunuel please edit the question stem, it must be "x percent more"

Bunuel · Answer

Thank you! Edited the typo.

keats · Answer

93 –10^3
94 – 10^3(1+x/100) 
95- 10^3(1+y/100)(1+x/100)

To calculate: 10^3 ( 1 + 1/10^2(x + y +xy/10^2))

Clearly B is sufficient

SonofAnarchy · Answer

hey,
i have a query.
we substituted the value of "xy" in the equation and are left with two unknown variable x and y.
Cant we substitute the value x=20/y also in the equation and make it a single variable equation?
From that we can find the value of x and y separately.

adiagr · Answer

1993: 1000

1994: 1000*( 1+ \frac{x}{100} )

1995: {1000*( 1+ \frac{x}{100} )} *( 1+ \frac{y}{100} )

value of xy alone would not serve our purpose.

B is sufficient.

KarishmaB · Answer

For anyone having the same query:

You have xy = 20

Number in 1995 = 1000 * (1 + x/100 + y/100 + xy/10000)

You can put x = 20/y and get:

Number in 1995 =  1000 * ( 1 + 20/100y + y/100 + 20/10000)

What next? We still have an unknown variable y. This is not an equation that will help you solve for y. You need to find the value of the highlighted expression. Also, even if this were an equation, it is likely to give you multiple values of y.

Another thing you can note is that xy = 20 means there are multiple values of x and y possible. e.g. x = 2, y = 10 or x = 4, y = 5 etc.
The value of the expression will change depending on which pair you take since x + y is different in each case.

iliavko · Answer

How can this be done in 2 minutes?.. The factoring is super difficult. Is this a 600 Q?..

KarishmaB · Answer

You have to do no factorisation here. Just realise that it is a question involving successive percentage changes. You can calculate that using the formula 
x + y + xy/100

Stmtn 2 gives you this value.

Stmnt 1 gives you xy = 20 only. In this case, x + y can take different values (1+20 or 2+10 or 4+5 etc). So the expression given above will have different values.

gmatassassin88 · Answer

option B tells from 1993 to 1995 there is increment of 9.2% in production of cameras i.e 1000*9.2%, final production 1092.

However questions asks how many cameras produced in the year 1995 and not the final production  VeritasKarishma

Kindly help

ccooley · Answer

The 1,092 number is the number produced in 1995. The statement tells you that the number produced in 1995 (in other words, (1+x/100)*(1+y/100)*1000) is 9.2% greater than the number produced in 1993. So, because you know the number produced in 1993, you can now find the number produced in 1995.

For instance, if you bake 10 cookies today, and you bake 40% more cookies tomorrow, the number of cookies you bake tomorrow is 14.

KarishmaB · Answer

Production per year is not a cumulative concept. 
When we say "from 1993 to 1995, the production increased by 9.2%, it means if production in 1993 was 1000, production in 1995 is 1092.
This does not mean that in 1995, only 92 cameras were produced. It means in 1995, 1092 cameras were produced.

MartyMurray · Answer

A manufacturer produced x percent more video cameras in 1994 than in 1993 and y percent more in 1995 than in 1994. If the manufacturer produced 1,000 video cameras in 1993, how many video cameras did the manufacturer produce in 1995?

(1) xy = 20
(2) x + y + xy/100 = 9.2

We are given the number of cameras produced in 1993.

Information on the percentage increase for each of the two years or the overall percentage increase for the entire two years would enable determining the number produced in 1995.

(1) xy = 20

There are infinite different values of x and y that could multiply to 20.

For example, x = 5, and y = 4, or x = 0.1, and y = 200.

Different values of x and y lead to different numbers produced in 1995.

Insufficient.

(2) x + y + xy/100 = 9.2

When we see an equation like this one as a statement in a Data Sufficiency question, a good way to determine whether the statement is sufficient for answering the question is to determine what the formula represents.

In this case, per the passage, x and y represent the percentage changes for 1994 and 1995.

So, to determine what the formula represents, we have only to identify what xy/100 represents.

x * y/100 is y percent of x.

So, what we can recognize is that y percent of x is the percentage increase for the second year attributable to the compounding effect of first increasing by x and next increasing by y.

So, we see that the equation presents the following:

1994 percent increase + 1995 percent increase + 1995 additional percent increase due to compounding = 9.2

So, 9.2 represents that total percentage by which the quantity increases from 1993 to 1995.

Of course, this percentage is sufficient for determining the quantity produced in 1995.

Sufficient.

Correct answer:   B

A manufacturer produced x percent more video cameras in 1994 than in

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